Analyses of the global process of glacial isostatic adjustment and post-glacial relative sea-level change continue to deliver important insights into Earth system form and process. One successful model of the related phenomenology is based upon a spherically symmetric internal viscoelastic structure for the solid Earth, which has been denoted VM2, and a model of the most recent deglaciation event of the current ice-age, denoted ICE-4G. The primary purpose of this paper is to describe several new a posteriori tests that have recently been performed to further investigate the quality of this global ‘solution’ to the inverse problem for both mantle viscosity and deglaciation history that is posed by the observables associated with this large-scale geodynamic phenomenon. I focus especially upon the ‘misfits’ of observations to the theoretical predictions of this model, which I am currently using to further refine its properties, and upon predictions made using it of geophysical signals that should soon become visible in the context of the Gravity Recovery and Climate Experiment (GRACE) satellite mission. Among the required refinements to ICE-4G, one that is necessary to eliminate a recently revealed misfit to space geodetic constraints on the present-day rate of radial motion at the Yellowknife location well to the west of Hudson Bay, and a similar misfit to absolute gravity measurements to the southwest of the Bay, is the insertion of a ‘Keewatin Dome’ of thick ice centred over Yellowknife with a ridge of ice extending to the south east. In the geomorphological literature, the existence of such a Keewatin Dome previously has been hypothesised but chronological control was lacking on the surface features that suggested its former existence. An important additional constraint that requires the late glacial existence of this important feature consists of new inferences of the Last Glacial Maximum lowstand of the sea from sites in the far field of the main concentrations of land ice.